一种基于多尺度核学习的仿射投影滤波算法

为了提高强非线性信号的噪声消除和信道均衡能力，在核学习自适应滤波方法的基础上，该文提出一种基于惊奇准则的多尺度核学习仿射投影滤波方法(SC-MKAPA)。在核仿射投影滤波算法的基础上，对核组合函数结构进行改进，将多个不同高斯核带宽作为可变参数，与加权系数共同参与滤波器的更新；利用惊奇准则将计算结果稀疏化，根据仿射投影算法的约束条件对惊奇测度进行改进，简化其方差项，降低了计算的复杂度。将该算法应用于噪声消除、信道均衡以及MG时间序列预测中，与多种自适应滤波算法及核学习自适应滤波算法进行仿真结果的对比分析，验证了该算法的优越性。

An Affine Projection Algorithm with Multi-scale Kernels Learning

In order to improve the ability of noise elimination and channel equalization of strong non-linear signals, a Multi-scale Kernels learning Affine Projection filtering Algorithm based on Surprise Criterion (SC-MKAPA) is proposed on the basis of kernel learning adaptive filtering method. Based on the kernel affine projection filtering algorithm, the structure of the kernel combination function is improved, and the bandwidths of several different Gaussian kernels are taken as variable parameters to participate in the update of the filter together with the weighted coefficients.The calculation results are sparsed by using the surprise criterion, and the surprise measure is improved according to the constraints of the affine projection algorithm, which simplifies the variance term and reduces the calculation complexity. The algorithm is applied to noise cancellation, channel equalization, and Mackey Glass (MG) time series prediction. The simulation results are compared with the traditional adaptive filtering algorithm and the kernel learning adaptive filtering algorithm, it proves the superiority of the proposed algorithm.